python-3.x - Pythonでキャニーエッジ検出器の方向を量子化する方法

Question

Rosettacode.org で見つけた Python での Canny 演算子のこの実装を理解しようとしていますが、thetaQ の計算方法がわかりません。この数式で 5 を使用する理由と、方向を量子化する方法を教えてください。誰でも私を助けてもらえますか？

#!/bin/python
import numpy as np
from scipy.ndimage.filters import convolve, gaussian_filter
from scipy.misc import imread, imshow

def CannyEdgeDetector(im, blur = 1, highThreshold = 91, lowThreshold = 31):
    im = np.array(im, dtype=float) #Convert to float to prevent clipping values

    #Gaussian blur to reduce noise
    im2 = gaussian_filter(im, blur)

    #Use sobel filters to get horizontal and vertical gradients
    im3h = convolve(im2,[[-1,0,1],[-2,0,2],[-1,0,1]]) 
    im3v = convolve(im2,[[1,2,1],[0,0,0],[-1,-2,-1]])

    #Get gradient and direction
    grad = np.power(np.power(im3h, 2.0) + np.power(im3v, 2.0), 0.5)
    theta = np.arctan2(im3v, im3h)
    thetaQ = (np.round(theta * (5.0 / np.pi)) + 5) % 5 #Quantize direction

    #Non-maximum suppression
    gradSup = grad.copy()
    for r in range(im.shape[0]):
        for c in range(im.shape[1]):
            #Suppress pixels at the image edge
            if r == 0 or r == im.shape[0]-1 or c == 0 or c == im.shape[1] - 1:
                gradSup[r, c] = 0
                continue
            tq = thetaQ[r, c] % 4

            if tq == 0: #0 is E-W (horizontal)
                if grad[r, c] <= grad[r, c-1] or grad[r, c] <= grad[r, c+1]:
                    gradSup[r, c] = 0
            if tq == 1: #1 is NE-SW
                if grad[r, c] <= grad[r-1, c+1] or grad[r, c] <= grad[r+1, c-1]:
                    gradSup[r, c] = 0
            if tq == 2: #2 is N-S (vertical)
                if grad[r, c] <= grad[r-1, c] or grad[r, c] <= grad[r+1, c]:
                    gradSup[r, c] = 0
            if tq == 3: #3 is NW-SE
                if grad[r, c] <= grad[r-1, c-1] or grad[r, c] <= grad[r+1, c+1]:
                    gradSup[r, c] = 0

.........